MRI contrast enhancement agents are frequently used in clinical settings to reduce MRI data acquisition times, selectively label certain tissues or organs, or enhance the observed contrast between similar soft tissues. Contrast enhancement agents are typically injectable solutions of transition metal ions complexed by ligands or bound to polymers. The transition metal ions offer a strong relaxation enhancement effect due to their large magnetic moment, and binding these ions to polymers often magnifies this effect. This so-called proton relaxation enhancement effect has been known for a long time, but a rigorous, quantitative theory and supporting computational framework needed for the rational design of contrast enhancement agents has been lacking. We are adapting computational techniques to the rational design of polymer bound transition metal complexes for use as contrast enhancement agents. During this study and later followup studies it was conclusively shown that the usual theoretical formalism used to analyze experimental data on these systems is qualitatively and quantitatively incorrect. However, it was demonstrated that it is possible to adapt the theoretical and computational techniques developed by Freed and co-workers to this problem thereby providing basis for the rational design of efficient contrast enhancement agents.